Write an exponential function to model the following situation.
A population of 130,000 grows 3% per year for 16 years.
How much will the popluation be after 16 years?
Write an exponential function in terms of x.
y=10
Answers
Answer:
y = 130,000(1.03)ˣ
Step-by-step explanation:
The general form of an exponetial function is y = abˣ, where a is the initial value (when x = 0), and b is the multiplier (the growth or decay factor). Here, we start with a population of 130,000, so our initial value a = 130,000. A growth of 3% each year represents a growth factor of 1.03, so after x years, the population y should be y = 130,000(1.03)ˣ.
The exponential function in terms of x and y is y = 130,000(1.03)ˣ
What is an exponential function ?The exponential function is a mathematical function denoted by
y = abˣ
where a is the initial value (when x = 0)
and b is the multiplier (the growth or decay factor).
population starts from 130,000, so
Initial value a = 130,000.
A growth of 3% each year represents a growth factor of 1.03,
so after x years, the population y should be
y = 130,000(1.03)ˣ
Therefore , The exponential function in terms of x and y is y = 130,000(1.03)ˣ
To know more about exponential function
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Related Questions
PLSSS HELP!! I'LL GIVE BRAINLIEST IF RIGHT Which is the equation of a parabola with a directrix at y = 2 and a focus at (5, 0). A) y = one fourth(x − 5)2 + 1 B) y = one fourth(x + 1)2 − 5 C) y = −one fourth(x + 1)2 − 5 d) y = −one fourth(x − 5)2 + 1
Answers
Answer:
The answer is below
Step-by-step explanation:
A parabola is the locus of a point such that its distance from a given line (directrix) and a fixed point (focus) is always the same.
The equation of a parabola with a horizontal line as directrix is given by:
(x - h)² = 4p(y - k)
where y = k - p is the directrix and the focus = (h, k + p)
Given that parabola has a directrix at y = 2 and a focus at (5, 0)
Therefore:
y = k - p
k - p = 2 (1)
focus = (h, k + p) = (5, 0)
h = 5, k + p = 0
k + p = 0 (2)
Solve equation 1 and 2 simultaneously by adding both equations together:
2k = 2
k = 1
Substitute k = 1 in k + p = 0 to find p:
1 + p = 0
p = -1
Therefore h = 5, p = -1 and k = 1
Substitute the values of h, k and p into the equation of a parabola:
(x - h)² = 4p(y - k)
(x - 5)² = 4(-1)(y - 1)
(x - 5)² = -4(y - 1)
x² - 10x + 25 = -4y + 4
-4y = x² - 10x + 21
4y = 10x - x² - 21
Mr. Smith has 78 total textbooks in his classroom cupboards. If the ratio of Science
books to ELA books is 5 to 8, how many Science books does he have?
38
0 48
O 30
65
Answers
In the function y= 1/3x^2,
what effect does the number 1/3 have on the graph,
as compared to the graph of the function y= x^2
A. It stretches the graph horizontally by a factor of 3.
B. It shrinks the graph horizontally to 1/3 its original width.
C. It shrinks the graph vertically to 1/3 its original height.
D. It stretches the graph vertically by a factor of 3.
Answers
1. Which expression can be factored into the form (ax + b)(ax - b), where
a and b are rational numbers?
4n2 - 81
2n2 - 49
2n2 + 49
4n2 + 81
Answers
The expression that can be factored into the form (ax + b)(ax - b), where a and b are rational numbers, is 4n² - 81.
What are the factors?A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.
Here,
A.
4n² - 81,
This can be factored as (2n - 9)(2n + 9), which is of the form (ax + b)(ax - b).
B.
2n² - 49,
This can be factored as (n - 7√2)(n + 7√2), but not in the form (ax + b)(ax - b).
C.
2n² + 49:
This cannot be factored into the form (ax + b)(ax - b) using rational numbers. We can factor it over the complex numbers as (n + i√49/2)(n - i√49/2), where i is the imaginary unit, but this does not satisfy the conditions of the problem.
D.
4n² + 81,
This cannot be factored into the form (ax + b)(ax - b)
Therefore, the expression that can be factored into the form (ax + b)(ax - b), where a and b are rational numbers, is 4n2 + 81.
Learn more about Factors here:
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Which statement is true??
Answers
A bag contains:
• 5 red marbles
• 6 blue marbles
• 3 green marbles
• 4 black marbles
• 2 yellow marbles
A marble will be drawn from the bag and replaced 100 times. What is a reasonable prediction for the number of times a green or black marble will be drawn?
Answers
Answer:
35/100
Step-by-step explanation:
P(green or black) = 3/20 + 4/20 = 7/20
7/20 = 35/100
Answer:
35 times
Step-by-step explanation:
all of them added together is 20 7/20 7x5=35 because 20 goes into 100 5 times
35 is 29% of what number
Answers
Answer:
10.15 is 29% of 35.
Step-by-step explanation:
(11 + 5) - 7(2 - 1) - 4
show work
Answers
Answer:
answer is 5 hope it helps
Answer:
5
Step-by-step explanation:
11+5=16
2-1=1
(16)-7(1)-4
16-7-4
16-7-4=5
What is the slope of this graph?
A. -4
B. 1/4
C. -1/4
D. 4
Answers
Answer:
-4 is the slope
Step-by-step explanation:
Because the line is going downwards that makes it a negative and if you count the boxes rise over run. You look for the point where the line meets a box perfectly and then you count the boxes down which is 4 and across which is one which makes it -4/1. So the slope is -4.
WILL MARK BRAINLIEST PLEASE PLEASE solve the inequality for x. -2x - 2 < 8
Answers
Answer:
Step-by-step explanation:
we will add like terms
-2x-2<8
we will add 2 on both sides
-2x<10
divide by 2
-x<5
multiply by -1
x>-5
Help please i dont get it
Answers
Answer:
3.51
Step-by-step explanation:
yes
Answer:
3.28
Step-by-step explanation:
Light travels at a speed of 1.8 x 10^7 miles per second. Pluto's average distance from the sun is 3,600,000,000 miles. on average how long does it take sunlight to reach Pluto?
Answers
Answer:
5 hours 8 mins?
Step-by-step explanation:
Jerry had k pencils. darcy and leonard then gave jerry an additional x pencils each. which expression could represent the number of pencils jerry has now?
Answers
Answer:
[tex]k[/tex]+([tex]x[/tex]×[tex]x[/tex])
Step-by-step explanation:
k is the number of pencils jerry has, and x is the number of pencils darcy and leonard gave him EACH. So you need to multiply 'x' x2 to get the total ammount of pencils they gave him, then add 'k' to know how much in total he has now.
hope it helped! (3
PLS HELP ME ASAP I DONT HAVE TIME. IT ALSO DETECTS IF ITs RIGHT OR WRONG.
Answers
Answer:
10
Step-by-step explanation:
2pi(5) is 31.42.
31.42/pi gets you exactly 10pi meters.
Anyone know the correct answer?!
Answers
Answer: Lower-right corner [tex]3^7 \times \frac{1}{3^4}[/tex]
Explanation:
We use the rule that
[tex]a^{-b} = \frac{1}{a^b}[/tex]
The negative exponent tells us to apply the reciprocal if we want the exponent to be positive.
In this case, a = 3 and b = 4
So,
[tex]a^{-b} = \frac{1}{a^b}\\\\3^{-4} = \frac{1}{3^4}[/tex]
which is why overall,
[tex]3^7\times 3^{-4} = 3^7 \times \frac{1}{3^4}[/tex]
a) x² when x = 6
b) y² when y= -9
c) z² when z = 0.7
Answers
Answer:
a)36
b)-81
c)0.49
Hope it helps..
HELP I NEED HELP ASAP
Answers
I think the answer is A
A population of 35 foxes in a wildlife preserve doubles in size every 15 years. the function y=35•2^x , where x is the number of 15-year periods, models the population growth. how many foxes will be after 45 years?
Answers
Answer:
reee
Step-by-step explanation:
skreeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
105
Step-by-step explanation:
15×3
45
35×3=105
Part A The ordered pair that represents the intersection of the x-axis and y-axis is called the _ A endpoint B origin C x coordinate D y coordinate. Part B the coordinates of the origin are _ A (1,1) B (0,1) C (0,0) D (1,0) I will give 15 brain
Answers
Answer: Part A. B origin Part B. C(0,0)
Step-by-step explanation:
In a coordinate plane, there are two axes
1) x-axis which is the horizontal axis.
2) y-axis which is the vertical axis.
The intersection of both the axes is known as the origin whose coordiantes are (0,0), i.e. at this point value of x =0 and value of y =0.
Part A: The ordered pair that represents the intersection of the x-axis and y-axis is called the origin.
Part B: The coordinate. Part B the coordinates of the origin are (0,0).
Answer:
A 1,1
Step-by-step explanation:
PLSS HELP ME!! ASAP!! I WILL GIVE YOU BRAINLYEST!!
What is the best estimate of the area of the figure in square inches?
Answers
To find the area of this figure the best action would to divide it into three different sections, finding the area of each and then adding them all together.
First, find the area of the square in the center, which would be 60in.
Second, find the area of the half circle. You would use the formula for area of a circle. You would divide this answer by 2 since this is only half of a circle. You would get 14.135in.
Last, you would find the area of the triangle. You would multiply both sides and then divide by 2, since it’s a triangle and not a square. Area for this is 12in.
And then you would add all these together.
Answer:
86.1372 -------> 86.1 (Nearest Tenths)
86.1372 -------> 86.14 (Nearest Hundreths)
86.1372 --------> 86.137 (Nearest Thousandths)
Step-by-step explanation:
Semicircle: 3.14*[tex]3^{2}[/tex]/2 = 14.1372
Triangle: 4*6 = 24/2 = 12
Rectangle: 10*6 = 60
14.1372 + 12 + 60 = 86.1372
86.1372 -------> 86.1 (Nearest Tenths)
86.1372 -------> 86.14 (Nearest Hundreths)
86.1372 --------> 86.137 (Nearest Thousandths)
duane spins a fair spinner what is the probability it will land on 4 write your answer as a decimal
Answers
Answer:
Give me what the steps are what are the numbers
Step-by-step explanation:
If 7x−6y=2 and −2x−y=3 are true equations, what would be the value of 5x−7y?
Answers
Answer:
-55
Step-by-step explanation:
7x-6y=2
-2x-y=3
by substitution method
y=3+2x
7x-6(3+2x)=2
7x-18-12x=2
-5x=20
x=-4
-2(-4)-y=3
8-y=3
-y=3-8
y=5
therefore the value of x=4 and that of y=5
5x-7y=5(-4)-7(5)
=-20-35
=-55
PLEASR HELP ASAP!!!!!!! i’ll mark brainlest
Answers
That’s the answer I think
what is the mesuement for y
Answers
Answer:
60 degrees
Step-by-step explanation:
add all together
make an equation of the sum= 180
this would mean 9r-9=180
solve
9r-9=180
9r=189
r=21
plug 21 in for r on the angle Y
solve
3(21)-3
63-3
60
A car travels for 4 hours at an average speed of 45mph and then 6hours at an average speed of 35mph. Work out the distance travelled.
Answers
Answer:
390 miles
Step-by-step explanation:
(45 x 4) + (35 x 6) = 390 miles
The scale of a map is 1:4 000 000. Hint: 1:4 000 000 means that 1cm on the map = 4 000 000 on the ground. The distance between Leeds and London on this map is 8.125cm. Calculate the actual distance between Leeds and London. Give your answer in kilometres.
Answers
Answer:
325 km
Step-by-step explanation:
Given the scale :
1 : 4 ,000, 000
1cm measure in map = 4000000 on the ground
From the map :
Distance between Leeds and London = 8.125 cm
The actual distance on ground can be calculated thus :
1cm = 4,000,000
8.125cm = x
Cross multiply
x = 32500000 cm
Converting to kilometers :
1 km = 100,000 cm
x = 32500000
Cross multiply
100,000x = 32500000
x = 32500000 / 100000
x = 325
Hence, actual distance between Leeds and London is 325 km
write this number in standard form.
(7 x 100) + (4 x 100 ) + (8 x 1,000)
help asap.
this is a 5th grader problem.
thank you.
worth 50 points!
Answers
Answer:
(7 x 100) + (4 x 100 ) + (8 x 1,000)
=700+400+8000
=1100+8000
=91009100 is the right answer.00:00
A company loses $5,400 as the result of a manufacturing defect. The 8 owners of the company must share the loss equally.
Part A
Which expression shows the change in profit for each owner?
O A. -5,400 + 8
O B. -5,400 - 8
OC -5,400.8
OD. -5,400 + 8
Which expression explains how to split the debt
Answers
Answer:
None of them. The proper expression(s) to split the debt are:
5400 / 8
or
8x=5400
(HURRY) Shanice won 88 pieces of gum playing the bean bag toss at the county fair. That was 4 more than twice as many as Greg. How many pieces of gum did Greg win? Which equation can be used to solve the problem?
Answers
Answer:
Greg won 42 pieces of gum
Step-by-step explanation:
Find the measure of each angle indicated. Show work.
Answers
Answer:
? = 109 degrees
Step-by-step explanation:
45 + 75 + _ = 180 ( look for vertical angles)
45 + 75 + 60 = 180
60 +79 + _ = 180 (look for a straight line that forms 180 degrees)
60 + 79 + 41 = 180
68 + 41 + _ = 180 (look for a triangle that adds up to 180)
68 + 41 + 71 =180
180 - 71 = 109 (look for a linear pair)
